Mister Exam

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Sum of series:
(2^n+(-1)^n)/5^n
(n+1)/5^n
(-1/2)^n
(5^n-4^n)/20^n
Identical expressions
one /(n*(n- one)*(n- two))
1 divide by (n multiply by (n minus 1) multiply by (n minus 2))
one divide by (n multiply by (n minus one) multiply by (n minus two))
1/(n(n-1)(n-2))
1/nn-1n-2
1 divide by (n*(n-1)*(n-2))
Similar expressions
1/(n*(n+1)*(n-2))
1/(n*(n-1)*(n+2))
1/n*(n-1)*(n-2)

Sum of series/ 1/(n*(n-1)*(n-2))

Sum of series 1/(n(n-1)(n-2))

The solution

You have entered [src]

  oo                   
 ___                   
 \  `                  
  \           1        
   )  -----------------
  /   n*(n - 1)*(n - 2)
 /__,                  
n = 1

$$\sum_{n=1}^{\infty} \frac{1}{n \left(n - 1\right) \left(n - 2\right)}$$

Sum(1/((n*(n - 1))*(n - 2)), (n, 1, oo))

The radius of convergence of the power series

Given number:
$$\frac{1}{n \left(n - 1\right) \left(n - 2\right)}$$
It is a series of species
$$a_{n} \left(c x - x_{0}\right)^{d n}$$
- power series.
The radius of convergence of a power series can be calculated by the formula:
$$R^{d} = \frac{x_{0} + \lim_{n \to \infty} \left|{\frac{a_{n}}{a_{n + 1}}}\right|}{c}$$
In this case
$$a_{n} = \frac{1}{n \left(n - 2\right) \left(n - 1\right)}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\left(n + 1\right) \left|{\frac{1}{n - 2}}\right|\right)$$
Let's take the limit
we find

True

False

The rate of convergence of the power series

The answer [src]

zoo

$$\tilde{\infty}$$

±oo

The graph

Examples of finding the sum of a series

The Sum of the Power Series
```
x^n/n
```
```
(x-1)^n
```
Factorial
```
1/2^(n!)
```
```
n^2/n!
```
```
x^n/n!
```
```
k!/(n!*(n+k)!)
```
Flint Hills Series
```
csc(n)^2/n^3
```
Basel problem
```
1/n^2
```
```
1/n^4
```
```
1/n^6
```
Harmonic series
```
1/n
```
Grandi's series
```
(-1)^n
```
Alternating series
```
(-1)^(n + 1)/n
```
```
(n + 2)*(-1)^(n - 1)
```
```
(3*n - 1)/(-5)^n
```
```
(-1)^(n - 1)*n/(6*n - 5)
```
Newton–Mercator series
```
(-1)^(n + 1)/n*x^n
```
Exam the series for convergence
```
(3*n - 1)/(-5)^n
```

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How to use it?

Identical expressions

Similar expressions

Sum of series 1/(n*(n-1)*(n-2))

The solution

Examples of finding the sum of a series

Sum of series 1/(n(n-1)(n-2))